Mohamed phd, Seid Asso. Prof.Yemane, Gediyon2022-01-282023-11-042022-01-282023-11-042011-01http://etd.aau.edu.et/handle/123456789/29777This project is a reading material in all Complx Analysis. it deals mainly with the class of Analytic Functions on an open set G. Our purpose is to desc ribe this class of analytic functions is complete metric space with dclincd metric space. As a consequence we prove the SCI of all continuous function is com plete metric space. Let 'F be family of analytic function in a region G. We prove that 'F is a normal famiey. provided that 'F is loca lly bounded. We also briefly discuss applications to the normal families of analytic func tionsenSpace of Analytic FunctionsThesis